At the risk of turning this into a sports thread, Ken Griffey Sr. was a very good ballplayer but Ken Griffey Jr. is a much better one (at least before injuries got to him).
Robert Downey, Jr. has contributed more to the culture than his dad, IMO, though since one’s an actor and the other is/was a director, I may be comparing apples to oranges.
Respecting Bob Dylan’s importance as an artist and as a songwriter, I always did prefer his son Jakob’s music, certainly his singing.
I like Hank Williams III better than his daddy, though not as much as his grandpa.
Drew remains my favorite Barrymore.
I like Natasha Richardson, Maya Rudolph, Rashida Jones and Gwyneth Paltrow better than any of their assorted parents.
Both Alessandro and Domenico Scarlatti were great composers, but in the end Domenico edged out his father, who was however more famous in their lifetimes.
Painter Artemisia Gentileschi was arguably a greater artist than her father Orazio.
Emmy and Max Noether were both notable mathematicians, but (as you can tell from the relative sizes of their Wikipedia articles) Emmy (Max’s daughter) is definitely the more famous one.
I don’t know about more talent but it is reported that Jack Cassidy was very jealous of the success and adulation of his son David Cassidy of “The Partridge Family” fame. A fine and respected old time actor Vs a pop teen music sensation who drew huge crowds.
Emily and Zooey Deschanel’s mother was an actress, but without any big, starring roles that I know of. (I liked her in The Right Stuff, though; my favorite movie.) Their father has been nominated for five Oscars as a cinematographer.
Gwyneth Paltrow is at least open for debate. She’s been very good in some roles, but she was the weak link in Sky Captain and the World of Tomorrow. She was too fragile and hesitant for the 1930’s, fast-talking, girl reporter role. Her mother would have been great.
I suppose it would depend on your point of view, but one could argue the Jean Renoir was greater (or, at least, his equal in his own field) than his father Pierre-August.
Fritz Leiber, Jr. (the science fiction writer) is definitely more talented than his father Fritz Leiber, Sr. (an actor of the 30s and 40s).
George M. Cohan definitely surpassed his father and his mother (both vaudevillians).
I prefer Loudon Wainwright III (who surpassed his father, a Life Magazine editor), but his children (Rufus Wainwright, Martha Wainwright, and Lucy Wainwright Roche) are probably better known and more successful now.
John Huston surpassed his father Walter. His daughter Angelica was also pretty good.
Ed Wynn was a famous vaudeville and radio star. Keenan Wynn was a fine character actor and a decent song and dance man. I can’t say more talented, but certainly more versatile.
Robert Alda was a leading man on Broadway. Alan Alda is certainly a better actor, although not as good at song and dance.
I think Bonnie Raitt is more talented than John Raitt, but I know there are a lot of Broadway lovers that would disagree.
Going back a few centuries, Alexandre Dumas pere wrote more novels, Alexandre Dumas fils wrote more (and better) plays. You be the judge.